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Is the UK now more likely to leave the EU?

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The long saga of U.K. membership of the European Union may end with a historic and traumatic as pro-Europeans face an onslaught from the Eurokeptic right – and now left.

The possibility of so-called Brexit appears to have been discounted by investors at the moment – but as the respective campaigns to leave or stay ramp up between now and whenever the vote happens (by the end of 2017), they are likely to take more notice.

On Tuesday, French bank Societe Generale made the risk of Brexit one of its "key calls" for investors, and said it would recommend reducing holdings in the pound and in U.K. shares amid the uncertainty prompted by the referendum.

After an era where U.K. politicians chased the center ground and those who raised the prospect of leaving the EU were regularly dismissed, those at the center now risk being confronted by an anti-EU pincer movement from both left and right.

Left-wing swing

The Labour Party has been pro-EU membership for decades, and was expected to broadly support the Stay campaign for the referendum. Yet with an influx of new members, a new, more Euroskeptic leader in Jeremy Corbyn, and the U.K.'s trade unions waging more power within the party than for decades, Labour cannot be automatically assumed to be on the EU side any more.

"We can't just give Cameron a blank cheque whatever he comes back with: we have to be fighting for the Europe that we want to see. He talked about...the importance of the social chapter, the EU working time directive," a Labour Party spokeswoman said of Corbyn's position on the EU.

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Pro-EU voices within the party, like former Shadow Business Secretary Chuka Ummuna, have stepped aside already over Corbyn's position.

Unite, one of the country's most powerful unions, has already said it would campaign for Brexit if the UK opts out of EU employment regulations. The issue could also be a vote-winner in some of Labour's northern constituencies where their vote share could be threatened by the U.K. Independence Party, which has long campaigned against the country's EU membership

Right-wing rumble

The threat of Brexit on the right has been visible for longer, but it is no less effective for that. Arguably, it was concerns about rising support for UKIP (which did not result in the expected number of parliamentary seats in May's general election) which drove the centrist Prime Minister to hold a potentially destabilizing referendum in the first place.

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While UKIP and the Leave campaign may not have been as visible in the past few months, they have been busy. What some analysts and experts might call an unholy alliance with voices on the Left could be next on their agenda.

- By CNBC's Catherine Boyle